The EMI Formula, Explained Line by Line

By Pradipta Ray · Published 23 September 2026

The EMI formula looks intimidating and is actually one line of arithmetic. This walks through what each part does and why it is shaped the way it is.

Here is the formula every Indian lender uses for a reducing-balance loan:

EMI = P x r x (1 + r)^n / ((1 + r)^n - 1)

Three inputs go in. P is the principal, the amount actually borrowed. r is the monthly interest rate, which is the annual rate divided by 12 and then by 100 - so 9% a year is 0.0075. n is the number of monthly instalments.

Skip the arithmetic and use the calculatorEMI Calculator

Why the formula is shaped like that

The formula answers a specific question: what fixed payment, made every month for n months, exactly clears a loan of P if interest accrues at r per month on whatever is left?

The term (1 + r)^n is what the principal would grow to if you paid nothing at all for n months. Dividing by ((1 + r)^n - 1) spreads that growth across the instalments. Multiplying by P x r scales it to your loan. Put together, they produce the one payment size that lands the balance on exactly zero at the end.

Computing it by hand

Take a five-lakh loan at 12% over five years.

Monthly rate: 12 / 12 / 100 = 0.01.
Number of months: 5 x 12 = 60.
(1 + r)^n = 1.01^60, which is about 1.8167.
Numerator: 500000 x 0.01 x 1.8167 = about 9,083.
Denominator: 1.8167 - 1 = 0.8167.
EMI = 9,083 / 0.8167, which is about 11,122.

The engine on this site computes the same loan to the paisa:

₹5,00,000 at 12% over 5 years, computed by the site's EMI engine.
	Amount
Monthly EMI	₹11,122
Total interest	₹1,67,338
Total repayment	₹6,67,338
Interest as a share of the loan	33%

₹5,00,000 at 12% over 5 years, computed by the site's EMI engine.

The 0% case

When the rate is zero, the formula breaks: r is 0, so the numerator is 0 and the denominator is 0. Mathematically you take the limit, and the answer is exactly what intuition says - the instalment is simply the amount divided by the number of months.

This is the case that matters for no-cost EMI offers on phones and appliances, where the instalments are just the price split evenly. What that split hides is covered in is no-cost EMI really free.

Running the formula backwards

The same relationship inverted tells you how much you can borrow for a given instalment:

P = EMI x ((1 + r)^n - 1) / (r x (1 + r)^n)

That is exactly how a lender sizes your loan: it decides what EMI your income can support, then works out the principal that instalment services. The Loan Eligibility Calculator does the same thing.

In a spreadsheet

Excel and Google Sheets have the formula built in as PMT. For a five-lakh loan at 12% over 60 months, use =PMT(0.12/12, 60, -500000). Note the negative principal - without it the result comes back negative.

One caution with PMT: it returns the unrounded instalment. Lenders round to the nearest rupee and adjust the final instalment, which is why a schedule built from an unrounded EMI drifts by a few rupees by the end.

Frequently asked questions

What is r in the EMI formula?

The monthly interest rate as a decimal: the annual rate divided by 12, then by 100. An annual rate of 9% gives r = 0.0075.

Can I use the same formula for a flat-rate loan?

No. A flat rate charges interest on the original principal for the whole tenure, so the instalment is (principal + total interest) / months. The two produce very different costs at the same quoted rate.

Which Excel function calculates EMI?

PMT. Use =PMT(annual_rate/12, months, -principal). It returns the unrounded instalment, so expect a small difference from a lender's rounded figure.